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We consider policy optimization for online episodic tabular Markov decision processes (MDPs) with adversarial losses and bandit feedback. Policy optimization updates the policy locally at each state and avoids optimization over the occupancy-measure polytope, but its existing regret bounds are larger by a factor of the...
We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks. The objective is the sum of a possibly nonsmooth nonconvex Lipschitz function and a convex regularizer, and the function is acces...
Muon has emerged as a strong optimizer for the matrix-valued parameters in large language model pretraining, approximately orthogonalizing its momentum with a few Newton-Schulz iterations. Existing theory either replaces this iteration with the exact polar factor it approximates, or treats its finite depth as an approx...
A learning algorithm for general optimization problems with linear objective functions that eliminates the need to solve inverse optimization problems, and achieves competitive performance in terms of regret compared with existing methods, while offering improved computational efficiency for certain classes of downstre...
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